A TRACON Controller working busy combined sectors reported a departing jet pilot reported a NMAC when they overtook a slower moving aircraft.

Narrative

I had been working for 10 mins in incredibly busy traffic. We were short staffed and sectors combined. Aircraft X departed SNA heading 177 per the SID. Aircraft Y was southbound but shouldn't have been. That aircraft should have been on heading 155 or 080. I saw the conflict late since my mind was racing and I was extremely busy with no help. I turned Aircraft X to a heading of 230. It didn't do much and Aircraft X ended up right behind and overtaking Aircraft Y doing 100 kts. Aircraft Y was not in a place I expected him to be. Aircraft X responded to a TCAS RA descending out of 3000. Lateral was close. The pilot later questioned how close it was making me think it was close enough for him to think Near Mid Air. Sectors were combined when they shouldn't have; but we had no staffing. We are asked to work in these conditions of intense traffic Monday through Friday and still the FAA has the audacity to schedule mandatory overtime? This is not sustainable for our mental health. The union uses a lot of controllers for other duties and details and don't prioritize the operation. Both FAA and Union need to do better. We want a normal life outside of work.Recommendation: Hire more people